How do you simplify 1- (sin^2 theta/ (1-cos theta))= -cos theta?

2 Answers
Mar 28, 2018

Please see below.

Explanation:

Here,

1-((sin^2theta)/(1-costheta))=-costheta

LHS=1-(sin^2theta/(1-costheta)xx(1+costheta)/(1+costheta))

=1-(sin^2theta(1+costheta))/(1-cos^2theta).....to (1-cos^2theta=sin^2theta)

=1-((cancelsin^2theta)(1+costheta))/(cancel(sin^2theta)

=1-(1+costheta)

=1-1-costheta

=-costheta

=RHS

Mar 28, 2018

-cos theta

Explanation:

Firstly take L.H.S.(left hand side),

i.e. LHS=1 - (sin^2theta/(1-costheta))

=1-[(1-cos^2theta)/(1-costheta)]

=1-[(1^2-(costheta)^2)/(1-costheta)]

=1-[(((1+costheta))(cancel(1-costheta)))/((cancel(1-costheta)))]

so after solving it will give,

=1-(1+costheta)

=1-1-costheta

which will give,

=-costheta

=RHS

hence proved.